Globally coupled parametrically forced logistic maps

In this study, we propose a parametrically forced logistic map and investigate its bifurcation. By carrying out computer calculations, unique bifurcations from period to chaos are observed. Furthermore, we investigate synchronization phenomena in globally coupled logistic maps which involving parametric force and confirm various kinds of synchronization phenomena. In the case of two coupled maps, in-phase synchronization of two maps is observed. In the case of three coupled maps, synchronization states are changed with increasing coupling intensity from asynchronous, self-switching of synchronization, synchronization of two among the three maps, to synchronization of all the maps. Finally, we investigate the influences of phase difference of parametric forces on synchronization. The maps can not be synchronized completely if phase difference exists between two parametric forces of the maps.